Re: focal length in multi-element lenses

Hello.

What are you looking for?. A mathematical formula to calculate the focal length of a lens based on the curvature of its elements?. A physical procedure to measure it for a specific specimen of a lens design?. Or yet something else?.

Bear in mind rarely a real lens behaves as an ideal one of its type would. The focus plane can be curved. Sometimes there is a noticeable difference for the plane of best sagittal focus to that of tangential focus, especially when the lens is operated far from the focusing distance it was designed to. For a given lens the plane of best focus can vary with aperture, that phenomenon is called focus shift. In any case but very rough measurements you will need a definition of focal length (Especially important for mathematical approaches). "the distance to where the rays converge" is useless. To quote some defects in this definition for a rigorous approach: First, the wave nature of light (Rather than rays) is noticeable in the photography as diffraction. There are also aberrations, which in geometrical optics means rays only approximately converge. We also have to account for dispersion for all but optical systems meant to be used with light within a narrow enough band (So it is designated monochromatic); that's generally not the case for photographic systems.

Optics is a board and deep enough branch of physics so that there are specific books. Maybe you would want to read a book about Optics. It's a very interesting topic to me at lest. Another, online resource (Albeit there are online libraries like http://gen.lib.rus.ec/) is http://toothwalker.org/optics.html.